Free Fall Calculator
Enter a drop height, time, or final speed — the other two solve instantly, and a live 3D drop plus charts show the motion. Full worked examples and a physics explainer are below.
Reviewed by the ToolNestr Editorial Team — July 2026
Enter any one value — the others solve instantly.
Live 3D drop
Drag to orbit (touch works too). The ball falls the height you enter; press Drop to replay.
Motion graphs
How free fall is calculated
The core idea in one line: a dropped object starts at rest and gains speed at a steady rate g, so the distance it covers grows with the square of the time while its speed grows straight in proportion to time.
Everything comes from the constant-acceleration kinematic equations with initial velocity zero. Each variable is defined right after it:
- h = ½ · g · t² — the distance fallen after time t. Here g is gravity (9.81 m/s² on Earth).
- v = g · t — the velocity after time t. Speed rises by g every second.
- v = √(2 · g · h) — the impact velocity after falling a height h, obtained by eliminating t between the two equations above.
Rearranged, the same three formulas let you start from whichever quantity you know: given a height, the fall time is t = √(2h / g); given a time, the height is ½gt²; given a final speed, the time is v / g. That is exactly what the calculator does.
Worked example 1 — drop from a cliff
Given: a stone is dropped from a 45 m cliff on Earth (g = 9.81 m/s²). Find the fall time and impact speed.
Worked example 2 — the same drop on the Moon
Given: the identical 45 m drop, but on the Moon (g = 1.62 m/s²). Gravity is about 6× weaker, so the fall is slower.
The time grows as 1/√g and the impact speed as √g, so a 6.05× weaker gravity gives a 2.46× longer fall and a 2.46× gentler landing. Tap "Moon" above to reproduce these numbers.
Two ideas that trip students up
1. Mass does not change the fall
The heavy red ball and the light blue ball are released together and stay level the whole way down — in a vacuum they hit the ground at the same instant, exactly as Apollo 15 showed with a hammer and a feather.
2. The gaps grow as odd numbers
Snapshots at equal time steps spread further and further apart on the way down — the spacing follows 1 : 3 : 5 : 7. That widening is what "accelerating" actually looks like.
A 20 m drop on different worlds
Same height, same physics — only g changes. Weaker gravity means a longer, gentler fall.
| World | gm/s² | Fall times | Impact speedm/s |
|---|---|---|---|
| Moon | 1.62 | 4.97 | 8.05 |
| Mars | 3.71 | 3.28 | 12.18 |
| Earth ★ | 9.81 | 2.02 | 19.81 |
| Jupiter | 24.79 | 1.27 | 31.49 |
★ Earth reference. Fall time scales as √(2h/g) and impact speed as √(2gh), so a 15× stronger gravity (Moon→Jupiter) shortens the fall ~3.9× and quadruples the landing speed.
Where free fall actually shows up
🏗️ Construction & workplace safety
A dropped tool from height gains dangerous speed fast: a spanner falling 20 m hits at ~20 m/s (72 km/h). Safety engineers use v = √(2gh) to size netting, exclusion zones and hard-hat ratings.
🪂 Skydiving & parachutes
The first seconds of a jump are near-ideal free fall before drag matters. Canopy designers need the deployment speed to work out the opening shock the fabric and jumper must survive.
🎢 Rides, stunts & games
Drop-tower rides, film stunt falls onto air bags, and the gravity in countless video games all run on h = ½gt². Getting the deceleration distance right is the difference between a thrill and an injury.
Common misconceptions
"Heavier things fall faster."
In a vacuum they don't — mass cancels out and everything accelerates at g. A bowling ball and a marble dropped together land together. The only reason a feather loses in air is drag, which this model ignores.
"An object falls a constant distance each second."
It falls further every second, because it keeps speeding up. The per-second distances follow 1 : 3 : 5 : 7 — the object covers 4.9 m in the first second but 34.3 m in the fourth.
"Doubling the height doubles the fall time."
Time grows with the square root of height, not linearly. Doubling the drop height multiplies the fall time by only √2 ≈ 1.41. To double the time you need four times the height.
"Free fall means weightless because there's no gravity."
It's the opposite — gravity is the only force acting. The floating "weightless" feeling comes from everything accelerating together, so there's no support force pushing back; gravity is fully present.
Assumptions — and where this model breaks down
This is the ideal (drag-free) free-fall model: exact in a vacuum and a good approximation for dense, compact objects over short drops. Its honest limits:
Air resistance is ignored
Real drag grows with speed and eventually balances weight at terminal velocity. Light or long-falling objects reach far lower speeds than the formula predicts.
Starts from rest
This calculator assumes zero initial velocity. If the object is thrown downward, add v₀: v = v₀ + gt and h = v₀t + ½gt².
Gravity is constant
g is treated as fixed. That holds near a planet's surface but not for falls from great altitude, where g weakens with distance.
Purely vertical
Any sideways motion turns the problem into projectile motion — but the vertical fall is still governed by these exact equations.
Formula sources & further reading
These are the standard constant-acceleration kinematics of introductory physics, traceable to:
- • OpenStax, University Physics Volume 1 — §3.5 "Free Fall" (free, peer-reviewed). openstax.org
- • Halliday, Resnick & Walker, Fundamentals of Physics — Chapter 2, Motion Along a Straight Line (Free-Fall Acceleration).
- • Serway & Jewett, Physics for Scientists and Engineers — Chapter 2, Freely Falling Objects.
Standard gravity g = 9.80665 m/s² (rounded to 9.81), per the CGPM definition. Results rounded to two decimal places.
How to use this calculator
Enter one value
Type the height, time, or final velocity. Leave the fields you want to find blank; switch metric/imperial with the toggle.
Read all three
Height, time and final velocity fill in together, and the 3D drop plus charts redraw to match.
Change worlds
Tap Moon, Mars or Jupiter to change g and see how the same drop plays out elsewhere.
Related tools
Frequently asked questions
What is free fall?
Free fall is the motion of an object under gravity alone, with no other force acting (air resistance neglected). In a vacuum every object falls at the same rate regardless of mass — a feather and a hammer dropped together land together.
What is the acceleration due to gravity?
On Earth g ≈ 9.81 m/s² downward, so a falling object's speed increases by 9.81 m/s every second. On the Moon g = 1.62 m/s²; on Mars 3.71 m/s²; on Jupiter about 24.79 m/s².
How far does an object fall in one second?
From rest, an object falls about 4.9 m in the first second (h = ½ · 9.81 · 1²), then 14.7 m in the next second, then 24.5 m in the third. The distance in each successive second follows the odd-number ratio 1 : 3 : 5 : 7.
Does a heavier object fall faster?
No. In the free-fall model mass cancels out of the equations, so all objects accelerate at g and reach the ground together. Mass only matters once air resistance is included, which this calculator ignores.
How is free fall related to projectile motion?
Free fall is exactly the vertical part of projectile motion. A ball thrown horizontally falls at the same rate as one simply dropped from the same height — both hit the ground at the same instant.
Why does a skydiver stop speeding up?
Air resistance grows with speed. When the upward drag equals the downward weight the net force is zero, acceleration stops, and the skydiver coasts at terminal velocity (~53 m/s belly-down). That regime is beyond this idealised, drag-free calculator.